Finite Group Databasebeta

← #15617404

Subgroups — #15617404

Order 2816.

2738 conjugacy classes of subgroups.

The subgroup lattice has 278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623350C211yesmaximal, characteristic
2C2×#41×Dic11C211yesmaximal, characteristic
3#13077182C2116yesmaximal, complemented
4#13077179C216yesmaximal, complemented
5C2×#10622731C216yesmaximal, complemented
6C2×C11×#568C211yesmaximal, characteristic
7C22×C11×#41C2211yescharacteristic
8C11×#568—28no—
9C2×C11×#131C2218yes—
10C22×C11×M16C2216yes—
11#41×Dic11C414yes—
12#41×Dic11C414yes—
13#41×Dic11C2218yes—
14#10623350—28no—
15C2×#67001C2218yes—
16C2×Q8×Dic11C412yes—
17C2×D4×Dic11C416yes—
18C2×#66979C2213yes—
19C22×C4×Dic11C2213yes—
20C22×#4318C2216yes—
21#10622732C22124yescomplemented
22#10622731C2214yes—
23#10622731C22112yes—
24#10622731C22124yescomplemented
25#10622715C22124yescomplemented
26C2×Dic11⋊C8C22124yescomplemented
27C2×C11×#41C2×C414yes—
28C2×C11×#41D418yes—
29C2×C11×#41Q818yes—
30C2×C11×#41C2314yes—
31C22×Q8×C11C2×C411yescharacteristic
32C22×D4×C11C2×C413yes—
33C23×C4×C11C2313yes—
34C23×Dic11C2×C416yes—
35C11×#131—232no—
36C2×C11×M16—224no—
37C2×C11×M16C2314yes—
38C2×C11×M16C23112yes—
39C22×C8×C11C23112yes—
40C2×C22⋊Dic11C2×C416yes—
41#67001—232no—
42Q8×Dic11C2×C418yes—
43Q8×Dic11C2×C418yes—
44D4×Dic11C2×C4124yes—
45D4×Dic11C2×C4124yes—
46#66979C2×C4112yes—
47#66979C23112yes—
48C2×C4⋊Dic11C2×C416yes—
49C2×C4×Dic11C2×C416yes—
50C2×C4×Dic11C2×C416yes—
51C2×C4×Dic11C2×C416yes—
52C2×C4×Dic11C2311yescharacteristic
53C2×C4×Dic11C2313yes—
54C2×C4×Dic11C23112yes—
55C2×#4318—224no—
56C2×#4318C2314yes—
57C2×#4318C23112yes—
58C22×C11⋊C8C23112yes—
59Dic11⋊C8C23116yes—
60Dic11⋊C8C23148yes—
61#60099—111nomaximal, Sylow
62C24×C11C22×C413yes—
63C11×#41C4⋊C4132yes—
64C11×#41C2×D4116yes—
65C11×#41C2×Q8116yes—
66C2×Q8×C11C4⋊C418yes—
67C2×Q8×C11C22×C414yes—
68C2×D4×C11C4⋊C4124yes—
69C2×D4×C11C22×C4112yes—
70C22×C4×C11C22×C413yes—
71C22×C4×C11C22×C416yes—
72C22×C4×C11C2×D4112yes—
73C22×C4×C11C2×Q8112yes—
74C22×C4×C11C2416yes—
75C22×C4×C11C2411yescharacteristic
76C22×Dic11—412no—
77C22×Dic11C22×C412yes—
78C22×Dic11C22×C4112yes—
79C22×Dic11C22×C416yes—
80C22×Dic11C22×C4112yes—
81C11×M16—28no—
82C11×M16—224no—
83C2×C8×C11—224no—
84C2×C8×C11C2418yes—
85C22⋊Dic11C22×C4124yes—
86C4⋊Dic11C22×C4124yes—
87C4×Dic11C22×C411yescharacteristic
88C4×Dic11C22×C411yescharacteristic
89C4×Dic11C22×C416yes—
90C4×Dic11C22×C4112yes—
91C4×Dic11C22×C4112yes—
92C4×Dic11C2412yes—
93C4×Dic11C2416yes—
94#4318—28no—
95#4318—224no—
96C2×C11⋊C8—224no—
97C2×C11⋊C8C2418yes—
98C2×#568—111no—
99C2×#568D1111yescharacteristic
100C2×C4×#41—111no—
101#2906—1116no—
102#2905—116no—
103C2×#423—116no—
104C23×C11—46no—
105C23×C11C2×C4⋊C4112yes—
106C23×C11C23×C416yes—
107C23×C11C23×C411yescharacteristic
108Q8×C11C2×C4⋊C4116yes—
109D4×C11C2×C4⋊C4148yes—
110C2×C4×C11C2×C4⋊C4112yes—
111C2×C4×C11C2×C4⋊C4124yes—
112C2×C4×C11C23×C411yescharacteristic
113C2×C4×C11C23×C416yes—
114C2×C4×C11C22×D4112yes—
115C2×C4×C11C22×D412yes—
116C2×C4×C11C22×Q812yes—
117C2×C4×C11C22×Q8112yes—
118C2×C4×C11C2511yescharacteristic
119C2×Dic11—24no—
120C2×Dic11—224no—
121C2×Dic11—412no—
122C2×Dic11—46no—
123C2×Dic11C23×C412yes—
124C2×Dic11C23×C4112yes—
125C2×Dic11C23×C412yes—
126C8×C11—28no—
127C11⋊C8—28no—
128C22×#41C2×D1111yescharacteristic
129#568—28no—
130#568—228no—
131C2×#131—118no—
132C2×#131C2×D1118yes—
133C22×M16—116no—
134C22×M16C2×D1116yes—
135C4×#41—118no—
136C4×#41—114no—
137C4×#41—114no—
138C2×C4×Q8—112no—
139C2×C4×D4—116no—
140C2×#117—113no—
141C22×C42—113no—
142#424—1124no—
143#424—1124no—
144#423—114no—
145#423—1112no—
146#423—1124no—
147C2×C4⋊C8—1124no—
148C22×C11—22no—
149C22×C11—212no—
150C22×C11—412no—
151C22×C11C22×C4⋊C412yes—
152C22×C11C22×C4⋊C4112yes—
153C22×C11C24×C411yescharacteristic
154C4×C11C22×C4⋊C412yes—
155C4×C11C22×C4⋊C4112yes—
156C4×C11C23×D411yescharacteristic
157C4×C11C23×Q811yescharacteristic
158Dic11—22no—
159Dic11—212no—
160Dic11#56814yescomplemented
161C2×#41Dic2218yes—
162C2×#41C4×D1114yes—
163C2×#41C22⋊D1118yes—
164C2×#41C22×D1114yes—
165C22×Q8C4×D1111yescharacteristic
166C22×D4C4×D1113yes—
167C23×C4—116no—
168C23×C4C22×D1113yes—
169#131—232no—
170#131—2232no—
171C2×M16—224no—
172C2×M16—114no—
173C2×M16—1112no—
174C2×M16—2224no—
175C2×M16C22×D1114yes—
176C2×M16C22×D11112yes—
177C22×C8—1112no—
178C22×C8C22×D11112yes—
179C4×Q8—118no—
180C4×Q8—118no—
181C4×D4—1124no—
182C4×D4—1124no—
183#117—1112no—
184#117—1112no—
185C2×C4⋊C4—116no—
186C2×C22⋊C4—116no—
187C2×C42—116no—
188C2×C42—116no—
189C2×C42—116no—
190C2×C42—113no—
191C2×C42—1112no—
192C2×C42—111no—
193C4⋊C8—1116no—
194C4⋊C8—1148no—
195C2×C11—22no—
196C2×C11—212no—
197C2×C11C23×C4⋊C411yescharacteristic
198C2×C11C2×#56812yes—
199C24C2×C4×D1113yes—
200#41Dic11⋊C4132yes—
201#41C2×Dic22116yes—
202#41C2×C22⋊D11116yes—
203C2×Q8Dic11⋊C418yes—
204C2×Q8C2×C4×D1114yes—
205C2×D4Dic11⋊C4124yes—
206C2×D4C2×C4×D11112yes—
207C22×C4—112no—
208C22×C4—1112no—
209C22×C4—116no—
210C22×C4—1112no—
211C22×C4—4412no—
212C22×C4C2×Dic22112yes—
213C22×C4C2×C4×D1113yes—
214C22×C4C2×C4×D1116yes—
215C22×C4C2×C22⋊D11112yes—
216C22×C4C23×D1111yescharacteristic
217C22×C4C23×D1116yes—
218M16—28no—
219M16—224no—
220M16—228no—
221M16—2224no—
222C2×C8—224no—
223C2×C8—118no—
224C2×C8—2224no—
225C2×C8C23×D1118yes—
226C4⋊C4—1124no—
227C22⋊C4—1124no—
228C42—111no—
229C42—111no—
230C42—116no—
231C42—1112no—
232C42—1112no—
233C42—112no—
234C42—116no—
235C11#6009911yescharacteristic, complemented, Sylow
236C23—46no—
237C23C2×Dic11⋊C4112yes—
238C23C22×C4×D1116yes—
239C23C22×C4×D1111yescharacteristic
240Q8C2×Dic11⋊C4116yes—
241D4C2×Dic11⋊C4148yes—
242C2×C4—112no—
243C2×C4—112no—
244C2×C4—1112no—
245C2×C4—224no—
246C2×C4—2224no—
247C2×C4—4412no—
248C2×C4—446no—
249C2×C4C2×Dic11⋊C4112yes—
250C2×C4C2×Dic11⋊C4124yes—
251C2×C4C22×Dic2212yes—
252C2×C4C22×Dic22112yes—
253C2×C4C22×C4×D1111yescharacteristic
254C2×C4C22×C4×D1116yes—
255C2×C4C22×C22⋊D11112yes—
256C2×C4C22×C22⋊D1112yes—
257C2×C4C24×D1111yescharacteristic
258C8—28no—
259C8—228no—
260C22—22no—
261C22—212no—
262C22—412no—
263C22C22×Dic11⋊C412yes—
264C22C22×Dic11⋊C4112yes—
265C22C23×C4×D1111yescharacteristic
266C4—114no—
267C4—222no—
268C4—2212no—
269C4C22×Dic11⋊C412yes—
270C4C22×Dic11⋊C4112yes—
271C4C23×Dic2211yescharacteristic
272C4C23×C22⋊D1111yescharacteristic
273C2—22no—
274C2—212no—
275C2C23×Dic11⋊C411yescharacteristic
276C2D11×#56812yes—
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC2×C11×#568C2
prime radicalC22×C11×#41C22
cosocleC2×C4×C11C25
hypercenterC2×#568D11
hypocenterC11#60099
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×#568

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #13077182C2semidirect
4. #13077179C2semidirect
5. C2×#10622731C2semidirect
21. #10622732C22semidirect
24. #10622731C22semidirect
25. #10622715C22semidirect
26. C2×Dic11⋊C8C22semidirect
160. Dic11#568semidirect
235. C11#60099semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106233502
C2×#41×Dic112
#130771822
#130771792
C2×#106227312
C2×C11×#5682
#6009911